"They feel that they're disenfranchised – that this is a movement that's going around with Democrat-controlled cities. That it dilutes why people work so hard to become citizens, it dilutes elections as well, too," he said.

"People want to make sure the elections are honest and fair and upheld," McCarthy added.

Democratic leaders scoffed at McCarthy's proposal, saying it's wasteful to use floor time on non-binding resolutions rather than bills that could become law.

"I would point out this is not a law, it’s a non-binding resolution. So there's a clear attempt to try to play gotcha with folks," said Rep. Linda Sánchez (D-Calif.), vice chair of the House Democratic Caucus, at the weekly Caucus press conference.

"And instead of wasting time on a non-binding resolution, I would like to see the Republicans focused on getting the seven unfinished spending bills done, so we can keep the lights on in government," she added.